A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 4 inches across at its opening and is 3 feet deep, where will the collected light be concentrated?
The cross-section of the paraboloid through the focus and the vertex of the paraboloid must be a parabola. Use a coordinate system where the vertex is V(0, 0) and the point P(3, 2) are located on the parabola.
The general equation of a parabola opening to the right is:
Use the coordinates of P to calculate p. (I've got )
Then the focus F is the point where all parallel light rays will be concentrated. F has the coordinates